Wireless receiver being capable of determining its velocity

ABSTRACT

A wireless receiver being capable of determining its velocity with respect to a number of wireless transmitters is provided. The wireless receiver includes a communication interface for receiving a number of carrier signals originating from the number of wireless transmitters, and a processor being configured to determine a number of carrier phases of the carrier signals at two different time instants, to determine a number of carrier phase differences from the determined number of carrier phases for each carrier signal between the two different time instants, to determine a location matrix indicating a geometric relationship between a location of the wireless receiver and a number of locations of the number of transmitters, and to determine the velocity of the wireless receiver upon the basis of the number of carrier phase differences and the location matrix.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/RU2013/000926, filed on Oct. 21, 2013, which is hereby incorporatedby reference in its entirety.

TECHNICAL FIELD

The present patent application relates to the field of wireless velocitydetermination.

BACKGROUND

Wireless velocity determination systems can be based on determining anumber of carrier phases of a number of carrier signals. For velocitydetermination of a wireless receiver, the number of carrier signals cane.g. be transmitted by a number of wireless transmitters and can bereceived by the wireless receiver in order to determine its velocity.

For determining the number of carrier phases, the wireless receiverusually comprises a number of phase locked loops. Disturbances in theoperation of a phase locked loop, e.g. caused by short term shading ormechanical shock, can result in a cycle slip of the phase locked loopand impede the determination of the velocity of the wireless receiver.

Common methods for detection of cycle slips in phase locked loops areusually highly dependent on the expected dynamics of the wirelessreceiver. Aggressive dynamics can cause a carrier phase variationmistakenly identified as a cycle slip causing a false alarm of a cycleslip detector. Common methods based on a simultaneous analysis of thewhole number of phase locked loops usually have either low probabilityof correct detection or high computational cost.

In Zhoufeng Ren, et al., “A Real-time Cycle-slip Detection and RepairMethod for Single Frequency GPS Receiver”, 2011, 2nd Int. Conf. onNetworking and Inf. Technol. IPCSIT, vol. 17, pp. 224-230, cycle slipsare analyzed separately in each phase locked loop.

SUMMARY

It is the object of the patent application to provide a wirelessreceiver being capable of determining its velocity with improved cycleslip robustness.

This object is achieved by the features of the independent claims.Further implementation forms are apparent from the dependent claims, thedescription and the figures.

The patent application is based on the finding that a compressivesensing based approach for detection and/or correction of a cycle slipin carrier phase determination can be applied.

According to a first aspect, the patent application relates to awireless receiver being capable of determining its velocity with respectto a number of wireless transmitters, the wireless receiver comprising acommunication interface for receiving a number of carrier signalsoriginating from the number of wireless transmitters, and a processorbeing configured to determine a number of carrier phases of the carriersignals at two different time instants, to determine a number of carrierphase differences from the determined number of carrier phases for eachcarrier signal between the two different time instants, to determine alocation matrix indicating a geometric relationship between a locationof the wireless receiver and a number of locations of the number oftransmitters, and to determine the velocity of the wireless receiverupon the basis of the number of carrier phase differences and thelocation matrix. Thus, a wireless receiver being capable of determiningits velocity with improved cycle slip robustness can be provided.

The wireless receiver and the wireless transmitters can be part of aglobal navigation satellite system (GNSS), e.g. a GPS navigationsatellite system, a GLONASS navigation satellite system, or a Galileonavigation satellite system.

The communication interface can be configured to convert the number ofcarrier signals from radio frequency domain into baseband domain. Thecommunication interface can comprise an analog-to-digital-converter, afilter, an amplifier, and/or an antenna for receiving the number ofcarrier signals.

The processor can be configured to execute a computer program.

The velocity of the wireless receiver can comprise a velocity value,e.g. 5 m/s, and/or a velocity direction, e.g. 45°. The velocity of thewireless receiver can be represented by a vector.

The carrier signals can be characterized by a corresponding carrierfrequency, e.g. 1.5 GHz or 1.6 GHz, and a corresponding carrier phase,e.g. 20° or 65°. The carrier signals can be modulated.

The carrier phases can be characterized by a corresponding phase angle,e.g. 25° or 55°. The carrier phases can further be characterized by acorresponding fraction relative to the corresponding wavelength, e.g. atenth or a third of the wavelength.

The carrier phase differences can be characterized by a correspondingphase difference angle, e.g. 1° or 5°. The carrier phase differences canfurther be characterized by a corresponding fraction relative to thecorresponding wavelength, e.g. a twelfth or a fifth of the wavelength.

The two different time instants can be characterized by a difference intime, e.g. 5 μs. The difference in time between the two different timeinstants can relate to a sampling time interval.

The location matrix can indicate a geometric relationship between thelocation of the wireless receiver and the number of locations of thenumber of transmitters. The location matrix can be a directional cosinematrix.

The geometric relationship between the location of the wireless receiverand the number of locations of the number of transmitters can relate tothe mutual distance and/or mutual angle between the location of thewireless receiver and the number of locations of the number oftransmitters.

The location of the wireless receiver and the number of locations of thenumber of transmitters can be characterized by a correspondingcoordinate in a coordinate system, e.g. a Cartesian (x, y, z) coordinatesystem.

In a first implementation form according to the first aspect as such,the processor is configured to determine the velocity of the wirelessreceiver upon the basis of an optimization procedure according to thefollowing equations:

δ φ^(k) − HY^(k) + d^((k)) = 0$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein δφ^(k) denotes a vector comprising the number of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, | |₁ denotes thel₁-norm of a vector, k denotes a time instant index, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. Thus,the velocity of the wireless receiver can be determined efficiently.

The cycle slip values can correspond to a missed and/or a skipped cycleof a determined carrier phase. For a full cycle of 360°, a cycle slipvalue of one can e.g. correspond to a determined carrier phase of 15°instead of 375° or vice versa.

The vector d^((k)) can be supposed to be sparse, i.e. the number of zeroentries can be supposed to be substantially larger than the number ofnon-zero entries.

In a second implementation form according to the first aspect as such orthe first implementation form of the first aspect, the processor isconfigured to determine the velocity of the wireless receiver upon thebasis of an optimization procedure according to the following equations:

δ φ^(k) − HY^(k) + d^((k)) = 0$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in Z^{n}}} \right.$

wherein δφ^(k) denotes a vector comprising the number of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, | |₁ denotes thel₁-norm of a vector, k denotes a time instant index, R⁴ denotes the4-dimensional set of real numbers, Z^(n) denotes the n-dimensionalinteger lattice and n denotes the number of wireless transmitters. Thus,the velocity of the wireless receiver can be determined efficiently.

The cycle slip values can correspond to a missed and/or a skipped cycleof a determined carrier phase. For a full cycle of 360°, a cycle slipvalue of one can e.g. correspond to a determined carrier phase of 15°instead of 375° or vice versa.

The vector d^((k)) can be supposed to be sparse, i.e. the number of zeroentries can be supposed to be substantially larger than the number ofnon-zero entries.

In a third implementation form according to the first aspect as such,the first implementation form of the first aspect or the secondimplementation form of the first aspect, the processor is configured todetermine the velocity of the wireless receiver upon the basis of anoptimization procedure according to the following equations:

δ φ^(k) − HY^(k) + d^((k)) = 0$\left. {d^{(k)}}_{p}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein δφ^(k) denotes a vector comprising the number of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, | |_(p) denotes thel_(p)-norm of a vector, k denotes a time instant index, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. Thus,the velocity of the wireless receiver can be determined efficiently.

The cycle slip values can correspond to a missed and/or a skipped cycleof a determined carrier phase. For a full cycle of 360°, a cycle slipvalue of one can e.g. correspond to a determined carrier phase of 15°instead of 375° or vice versa.

The vector d^((k)) can be supposed to be sparse, i.e. the number of zeroentries can be supposed to be substantially larger than the number ofnon-zero entries.

In a fourth implementation form according to the first implementationform of the first aspect, the second implementation form of the firstaspect or the third implementation form of the first aspect, theprocessor is configured to perform the optimization procedure using alinear programming method, a semi-integer linear programming method oran orthogonal matching pursuit method. Thus, the optimization procedurecan be performed using efficient optimization methods.

The linear programming method can be adapted to optimize a linearobjective function, subject to linear equality constraints and/or linearinequality constraints. The linear programming method can comprise asimplex method, and/or an interior point method.

The semi-integer linear programming method can be adapted to optimize alinear objective function, subject to linear equality constraints and/orlinear inequality constraints, wherein a number of variables can besupposed to be integers.

The orthogonal matching pursuit method can be adapted to optimize alinear objective function, subject to linear equality constraints and/orlinear inequality constraints. The orthogonal matching pursuit methodcan comprise a QR factorization or a QR decomposition of the locationmatrix.

The orthogonal matching pursuit method can further comprise an integersearch method, such as a zero-forcing (ZF) method, aminimum-mean-square-error (MMSE) method, a maximum-likelihood-decoding(MLD) method, and/or a spherical maximum-likelihood-decoding (MLD)method, at its last iteration.

In a fifth implementation form according to the first aspect as such orany preceding implementation form of the first aspect, the processor isconfigured to determine the number of carrier phases of the carriersignals by comparing the number of carrier signals with a number ofreference signals. Thus, the carrier phases can be determinedindependently for each carrier signal.

The reference signals can be characterized by a corresponding referencefrequency, e.g. 1.5 GHz or 1.6 GHz, and a corresponding reference phase,e.g. 0°. The reference signals can be modulated.

Comparing a carrier signal with a reference signal can comprisedetermining a phase shift between the carrier signal and the referencesignal. The phase shift between the carrier signal and the referencesignal can be determined e.g. by a phase detector.

In a sixth implementation form according to the first aspect as such orany preceding implementation form of the first aspect, the communicationinterface comprises a number of phase-locked-loops for receiving thenumber of carrier signals originating from the number of wirelesstransmitters. Thus, the carrier signals can be received in a carrierphase preserving manner.

The phase-locked-loops can comprise a variable frequency oscillatorand/or a phase detector. The phase-locked-loops can further comprise afeedback loop.

In a seventh implementation form according to the first aspect as suchor any preceding implementation form of the first aspect, thecommunication interface is configured to receive the number of carriersignals according to a frequency-division-multiple-access scheme,time-division-multiple-access scheme or a code-division-multiple-accessscheme. Thus, mutual interference of the carrier signals can be avoided.

The frequency-division-multiple-access scheme can be characterized byallocating different carrier frequencies to the carrier signalsoriginating from the wireless transmitters. Thefrequency-division-multiple-access scheme can allow a simultaneoustransmission of the carrier signals in time.

The time-division-multiple-access scheme can be characterized byallocating different time slots to the carrier signals originating fromthe wireless transmitters. The time-division-multiple-access scheme canallow allocating the same carrier frequency to the carrier signals.

The code-division-multiple-access scheme can be characterized byallocating the same carrier frequency to the carrier signals originatingfrom the wireless transmitters while allowing a simultaneoustransmission of the carrier signals in time by using a spread spectrumtechnique.

In an eighth implementation form according to the first aspect as suchor any preceding implementation form of the first aspect, thecommunication interface is configured to selectively receive a number ofcarrier signals having different carrier frequencies, carrier phasedifferences, or carrier phase Doppler frequencies. Thus, the carriersignals can be received and processed separately.

The selective reception of the carrier signals can comprise a selectivefrequency filtering and/or a selective time gating of the carriersignals.

The carrier phase Doppler frequencies can relate to a Doppler shift ofthe carrier frequencies due to a velocity of the wireless receiver withrespect to the number of wireless transmitters.

According to a second aspect, the patent application relates to a methodfor determining a velocity of a wireless receiver with respect to anumber of wireless transmitters, the method comprising receiving anumber of carrier signals originating from the number of wirelesstransmitters by the wireless receiver, determining a number of carrierphases of the carrier signals at two different time instants by thewireless receiver, determining a number of carrier phase differencesfrom the determined number of carrier phases for each carrier signalbetween the two different time instants by the wireless receiver,determining a location matrix indicating a geometric relationshipbetween a location of the wireless receiver and a number of locations ofthe number of transmitters, and determining the velocity of the wirelessreceiver upon the basis of the number of carrier phase differences andthe location matrix. Thus, a method for determining a velocity of awireless receiver with improved cycle slip robustness can be provided.

The wireless receiver and the wireless transmitters can be part of aglobal navigation satellite system (GNSS), e.g. a GPS navigationsatellite system, a GLONASS navigation satellite system, or a Galileonavigation satellite system.

The velocity of the wireless receiver can comprise a velocity value,e.g. 5 m/s, and/or a velocity direction, e.g. 45°. The velocity of thewireless receiver can be represented by a vector.

The carrier signals can be characterized by a corresponding carrierfrequency, e.g. 1.5 GHz or 1.6 GHz, and a corresponding carrier phase,e.g. 20° or 65°. The carrier signals can be modulated.

The carrier phases can be characterized by a corresponding phase angle,e.g. 25° or 55°. The carrier phases can further be characterized by acorresponding fraction relative to the corresponding wavelength, e.g. atenth or a third of the wavelength.

The carrier phase differences can be characterized by a correspondingphase difference angle, e.g. 1° or 5°. The carrier phase differences canfurther be characterized by a corresponding fraction relative to thecorresponding wavelength, e.g. a twelfth or a fifth of the wavelength.

The two different time instants can be characterized by a difference intime, e.g. 5 μs. The difference in time between the two different timeinstants can relate to a sampling time interval.

The location matrix can indicate a geometric relationship between thelocation of the wireless receiver and the number of locations of thenumber of transmitters. The location matrix can be a directional cosinematrix.

The geometric relationship between the location of the wireless receiverand the number of locations of the number of transmitters can relate tothe mutual distance and/or mutual angle between the location of thewireless receiver and the number of locations of the number oftransmitters.

The location of the wireless receiver and the number of locations of thenumber of transmitters can be characterized by a correspondingcoordinate in a coordinate system, e.g. a Cartesian (x, y, z) coordinatesystem.

The method for determining the velocity of the wireless receiver can beperformed by the wireless receiver according to the first aspect as suchor any implementation form of the first aspect.

Further features of the method for determining the velocity of thewireless receiver can result from the functionality of the wirelessreceiver according to the first aspect as such or any implementationform of the first aspect.

In a first implementation form according to the second aspect as such,determining the velocity of the wireless receiver is performed upon thebasis of an optimization procedure according to the following equations:

δ φ^(k) − HY^(k) + d^((k)) = 0$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$

wherein δφ^(k) denotes a vector comprising the number of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, | |₁ denotes thel₁-norm of a vector, k denotes a time instant index, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. Thus,the velocity of the wireless receiver can be determined efficiently.

The cycle slip values can correspond to a missed and/or a skipped cycleof a determined carrier phase. For a full cycle of 360°, a cycle slipvalue of one can e.g. correspond to a determined carrier phase of 15°instead of 375° or vice versa.

The vector d^((k)) can be supposed to be sparse, i.e. the number of zeroentries can be supposed to be substantially larger than the number ofnon-zero entries.

In a second implementation form according to the second aspect as suchor the first implementation form of the second aspect, determining thevelocity of the wireless receiver is performed upon the basis of anoptimization procedure according to the following equations:

δ φ^(k) − HY^(k) + d^((k)) = 0$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in Z^{n}}} \right.$

wherein δφ^(k) denotes a vector comprising the number of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, | |₁ denotes thel₁-norm of a vector, k denotes a time instant index, R⁴ denotes the4-dimensional set of real numbers, Z^(n) denotes the n-dimensionalinteger lattice and n denotes the number of wireless transmitters. Thus,the velocity of the wireless receiver can be determined efficiently.

The cycle slip values can correspond to a missed and/or a skipped cycleof a determined carrier phase. For a full cycle of 360°, a cycle slipvalue of one can e.g. correspond to a determined carrier phase of 15°instead of 375° or vice versa.

The vector d^((k)) can be supposed to be sparse, i.e. the number of zeroentries can be supposed to be substantially larger than the number ofnon-zero entries.

In a third implementation form according to the second aspect as such,the first implementation form of the second aspect or the secondimplementation form of the second aspect, determining the velocity ofthe wireless receiver is performed upon the basis of an optimizationprocedure according to the following equations:

δ φ^(k) − HY^(k) + d^((k)) = 0$\left. {d^{(k)}}_{p}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein δφ^(k) denotes a vector comprising the number of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, | |_(p) denotes thel_(p)-norm of a vector, k denotes a time instant index, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. Thus,the velocity of the wireless receiver can be determined efficiently.

The cycle slip values can correspond to a missed and/or a skipped cycleof a determined carrier phase. For a full cycle of 360°, a cycle slipvalue of one can e.g. correspond to a determined carrier phase of 15°instead of 375° or vice versa.

The vector d^((k)) can be supposed to be sparse, i.e. the number of zeroentries can be supposed to be substantially larger than the number ofnon-zero entries.

In a fourth implementation form according to the first implementationform of the second aspect, the second implementation form of the secondaspect or the third implementation form of the second aspect, theoptimization procedure is performed using a linear programming method, asemi-integer linear programming method or an orthogonal matching pursuitmethod. Thus, the optimization procedure can be performed usingefficient optimization methods.

The linear programming method can be adapted to optimize a linearobjective function, subject to linear equality constraints and/or linearinequality constraints. The linear programming method can comprise asimplex method, and/or an interior point method.

The semi-integer linear programming method can be adapted to optimize alinear objective function, subject to linear equality constraints and/orlinear inequality constraints, wherein a number of variables can besupposed to be integers.

The orthogonal matching pursuit method can be adapted to optimize alinear objective function, subject to linear equality constraints and/orlinear inequality constraints. The orthogonal matching pursuit methodcan comprise a QR factorization or a QR decomposition of the locationmatrix.

The orthogonal matching pursuit method can further comprise an integersearch method, such as a zero-forcing (ZF) method, aminimum-mean-square-error (MMSE) method, a maximum-likelihood-decoding(MLD) method, and/or a spherical maximum-likelihood-decoding (MLD)method, at its last iteration.

According to a third aspect, the patent application relates to acomputer program for performing the method according to the secondaspect as such or any implementation form of the second aspect whenexecuted on a computer. Thus, the method can be applied in an automaticand repeatable manner.

The computer program can be provided in form of a machine-readable code.The computer program can comprise a series of commands for a processorof the computer. The processor of the computer can be configured toexecute the computer program.

The computer can comprise a processor, a memory, and/or an input/outputmeans.

The patent application can be implemented in hardware and/or software.

BRIEF DESCRIPTION OF THE DRAWINGS

Further embodiments of the patent application will be described withrespect to the following figures, in which:

FIG. 1 shows a schematic diagram of a wireless receiver being capable ofdetermining its velocity with respect to a number of wirelesstransmitters;

FIG. 2 shows a schematic diagram of a method for determining a velocityof a wireless receiver with respect to a number of wirelesstransmitters;

FIG. 3 shows a schematic diagram of a system for velocity determinationof a wireless receiver;

FIG. 4 shows a schematic diagram of a system for velocity determinationof a wireless transmitter;

FIG. 5 shows a schematic diagram of distances versus time between awireless receiver and a wireless transmitter;

FIG. 6 shows a schematic diagram of distances versus time between awireless receiver and a wireless transmitter; and

FIG. 7 shows a schematic diagram of a carrier phase processing by afilter.

DETAILED DESCRIPTION

FIG. 1 shows a schematic diagram of a wireless receiver 100 beingcapable of determining its velocity with respect to a number of wirelesstransmitters. The wireless receiver 100 comprises a communicationinterface 101 and a processor 103.

The communication interface 101 can be configured to receive a number ofcarrier signals originating from the number of wireless transmitters.The communication interface 101 can be configured to convert the numberof carrier signals from radio frequency domain into baseband domain. Thecommunication interface 101 can comprise an analog-to-digital-converter,a filter, an amplifier, and/or an antenna for receiving the number ofcarrier signals.

The processor 103 can be configured to determine a number of carrierphases of the carrier signals at two different time instants, todetermine a number of carrier phase differences from the determinednumber of carrier phases for each carrier signal between the twodifferent time instants, to determine a location matrix indicating ageometric relationship between a location of the wireless receiver and anumber of locations of the number of transmitters, and to determine thevelocity of the wireless receiver upon the basis of the number ofcarrier phase differences and the location matrix. The processor 103 canbe configured to execute a computer program.

The communication interface 101 and the processor 103 can be connected.

The wireless receiver 100 and the wireless transmitters can be part of aglobal navigation satellite system (GNSS), e.g. a GPS navigationsatellite system, a GLONASS navigation satellite system, or a Galileonavigation satellite system.

The velocity of the wireless receiver 100 can comprise a velocity value,e.g. 5 m/s, and/or a velocity direction, e.g. 45°. The velocity of thewireless receiver 100 can be represented by a vector.

The carrier signals can be characterized by a corresponding carrierfrequency, e.g. 1.5 GHz or 1.6 GHz, and a corresponding carrier phase,e.g. 20° or 65°. The carrier signals can be modulated.

The carrier phases can be characterized by a corresponding phase angle,e.g. 25° or 55°. The carrier phases can further be characterized by acorresponding fraction relative to the corresponding wavelength, e.g. atenth or a third of the wavelength.

The carrier phase differences can be characterized by a correspondingphase difference angle, e.g. 1° or 5°. The carrier phase differences canfurther be characterized by a corresponding fraction relative to thecorresponding wavelength, e.g. a twelfth or a fifth of the wavelength.

The two different time instants can be characterized by a difference intime, e.g. 5 μs. The difference in time between the two different timeinstants can relate to a sampling time interval.

The location matrix can indicate a geometric relationship between thelocation of the wireless receiver 100 and the number of locations of thenumber of transmitters. The location matrix can be a directional cosinematrix.

The geometric relationship between the location of the wireless receiver100 and the number of locations of the number of transmitters can relateto the mutual distance and/or mutual angle between the location of thewireless receiver 100 and the number of locations of the number oftransmitters.

The location of the wireless receiver 100 and the number of locations ofthe number of transmitters can be characterized by a correspondingcoordinate in a coordinate system, e.g. a Cartesian (x, y, z) coordinatesystem.

FIG. 2 shows a schematic diagram of a method 200 for determining avelocity of a wireless receiver with respect to a number of wirelesstransmitters.

The method 200 comprises receiving 201 a number of carrier signalsoriginating from the number of wireless transmitters by the wirelessreceiver, determining 203 a number of carrier phases of the carriersignals at two different time instants by the wireless receiver,determining 205 a number of carrier phase differences from thedetermined number of carrier phases for each carrier signal between thetwo different time instants by the wireless receiver, determining 207 alocation matrix indicating a geometric relationship between a locationof the wireless receiver and a number of locations of the number oftransmitters, and determining 209 the velocity of the wireless receiverupon the basis of the number of carrier phase differences and thelocation matrix.

The method 200 can be performed by a processor of a wireless receiver.

The wireless receiver and the wireless transmitters can be part of aglobal navigation satellite system (GNSS), e.g. a GPS navigationsatellite system, a GLONASS navigation satellite system, or a Galileonavigation satellite system.

The velocity of the wireless receiver can comprise a velocity value,e.g. 5 m/s, and/or a velocity direction, e.g. 45°. The velocity of thewireless receiver can be represented by a vector.

The carrier signals can be characterized by a corresponding carrierfrequency, e.g. 1.5 GHz or 1.6 GHz, and a corresponding carrier phase,e.g. 20° or 65°. The carrier signals can be modulated.

The carrier phases can be characterized by a corresponding phase angle,e.g. 25° or 55°. The carrier phases can further be characterized by acorresponding fraction relative to the corresponding wavelength, e.g. atenth or a third of the wavelength.

The carrier phase differences can be characterized by a correspondingphase difference angle, e.g. 1° or 5°. The carrier phase differences canfurther be characterized by a corresponding fraction relative to thecorresponding wavelength, e.g. a twelfth or a fifth of the wavelength.

The two different time instants can be characterized by a difference intime, e.g. 5 μs. The difference in time between the two different timeinstants can relate to a sampling time interval.

The location matrix can indicate a geometric relationship between thelocation of the wireless receiver and the number of locations of thenumber of transmitters. The location matrix can be a directional cosinematrix.

The geometric relationship between the location of the wireless receiverand the number of locations of the number of transmitters can relate tothe mutual distance and/or mutual angle between the location of thewireless receiver and the number of locations of the number oftransmitters.

The location of the wireless receiver and the number of locations of thenumber of transmitters can be characterized by a correspondingcoordinate in a coordinate system, e.g. a Cartesian (x, y, z) coordinatesystem.

FIG. 3 shows a schematic diagram of a system 300 for velocitydetermination of a wireless receiver 100. The system 300 comprises awireless receiver 100, a first wireless transmitter 301, a secondwireless transmitter 303, a third wireless transmitter 305, an i^(th)wireless transmitter 307, an n^(th) wireless transmitter 309, and avelocity vector v 311. The wireless receiver 100 can comprise anantenna.

The wireless receiver 100 and the wireless transmitters 301, 303, 305,307, 309 can be located at fixed positions. The small arrows canindicate projections of the velocity vector v 311, shown as a largearrow, onto the line of sight (LOS) lines or vectors.

High precision velocity determination can be based on simultaneoustracking of a plurality of carrier phase Doppler frequencies, or carrierphase incremental in discrete time.

The wireless receiver 100 or mobile receiver can receive radio signalstransmitted by several wireless transmitters 301, 303, 305, 307, 309 ortransmitters T_(i), i=1, . . . , n. The total number of transmitters canbe n.

Each wireless transmitter 301, 303, 305, 307, 309 can emit radiofrequency or RF waves at the frequency f_(i), the wavelength can be

$\lambda_{i} = {\frac{c}{f_{i}}.}$The light speed can be c=299792458 m/s. The local clocks of the wirelesstransmitters 301, 303, 305, 307, 309 can be supposed to be synchronized.Each carrier wave signal received by the wireless receiver 100 can betracked by its own phase locked loop (PLL). Each PLL can generate acarrier phase measurement φ_(i) ^((k)) where k can be the number ofsequential time moments, k=1, 2, . . . .

The position of the wireless receiver 100 can be known and presented ina fixed coordinate frame by the vector X=(x,y,z)^(T), the symbol ^(T)can denote the matrix transpose. The wireless transmitters 301, 303,305, 307, 309 can be located at known positions X_(i)=(x_(i), y_(i),z_(i))^(T).

Then the position of the wireless receiver 100 can be connected with thecarrier phase of the ith wireless transmitters 301, 303, 305, 307, 309as:

${\varphi_{i}^{k} = {{\frac{1}{\lambda_{i}}\sqrt{\left( {x - x_{i}} \right)^{2} + \left( {y - y_{i}} \right)^{2} + \left( {z - z_{i}} \right)^{2}}} + N_{i} + {f_{i}\Delta^{k}} + ɛ_{i}^{k}}},$where Δ^(k) can be the shift between the local clocks of the receiverand local clocks of the wireless transmitters 301, 303, 305, 307, 309,N_(i) can be the carrier phase ambiguity which can be an unknown integervalue. Its nature can be in the difference between initial phases of theheterodyne of the wireless receiver 100 and the generator of thewireless transmitter 301, 303, 305, 307, 309. Moreover, PLL's trackingcarrier phase can be accurate up to an unknown number of cycles. Thiscan explain why ambiguity can take an integer value.

If the real time step τ, i.e. the time incremental between twosequential time instances k+1 and k, is sufficiently small, then thevelocity V^(k)=(v_(x) ^(k), v_(y) ^(k), v_(z) ^(k))^(T) vector can beconnected with the carrier phase measurement incremental as

$\begin{matrix}{{\delta\;\varphi_{i}^{k}} \equiv {\varphi_{i}^{k + 1} - \varphi_{i}^{k}} \approx {{\frac{\tau}{\lambda_{i}}h_{i}^{T}Y^{k}} + {\delta\; ɛ_{i}^{k}}}} & ({CPI})\end{matrix}$where Y^(k) can be a four dimensional vector comprising three entries ofthe velocity vector extended by a fourth component δΔ^(k)=Δ^(k+1)−Δ^(k)which can mean the clock rate.h_(i) can be the four dimensional vector

$h_{i} = {\begin{pmatrix}\frac{x - x_{1}}{L_{i}} \\\frac{y - y_{1}}{L_{i}} \\\frac{z - z_{1}}{L_{i}} \\1\end{pmatrix} - {{directional}\mspace{14mu}{cosines}\mspace{14mu}{vector}}}$withL_(i)=√{square root over ((x−x_(i))²+(y−y_(i))²+(z−z_(i))²)}—length ofthe line of sight (LOS).

The carrier phase incremental equations can be generalized in themeasurements equationδφ^(k) =HY ^(k)+ξ^(k)  (M)where H can be a n×4 matrix, each ith row comprising vectors

$\frac{\tau}{\lambda_{i}}{h_{i}^{T}.}$The equation (M) can be derived in assumption that the ambiguities N_(i)are constant and do not depend on time k.

Equation (M) can correspond to the case of an absence of cycle slips. Apresence of cycle slips in operation of one or several PLLs can suggestthe measurement modelδφ^(k) =HY ^(k) +d ^((k))+ξ^(k)  (MCS)wherein d^(k) can be a vector of integer valued cycle slips values.

Assuming that CSs can happen to only few of channels, ideally to nochannel, the vector d^(k) can be considered as sparse vector, i.e. zeroentries can dominate over non-zero in the sense adopted in thecompressive sensing literature. The methods developed in the compressivesensing field can be applied to the recovery of the cycle slips vector.Carrier phase measurements can be considered for analysis.

In the following, the system (MCS) will exemplarily be considered.Considering d^(k) as an error affecting only few of the linearequations, a linear programming decoding procedure can be applied. Inthis case, it looks like

$\begin{matrix}{{{{\delta\;\varphi^{k}} - {HY}^{k} + d^{(k)}} = 0},\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.,} & ({L1})\end{matrix}$where

${z}_{1} = {\sum\limits_{i = 1}^{n}{z_{i}}}$can be the l₁-norm of the vector. Restricting d^((k)) to the integervalues only, the following problem can be obtained:

$\begin{matrix}{{{{\delta\;\varphi^{k}} - {HY}^{k} + d^{(k)}} = 0},\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.,} & \left( {{L1}\text{-}{Integer}} \right)\end{matrix}$with notation Z^(n) standing for the integer lattice.

More generally, an l_(p) optimization problem, i.e.

${{z}_{p} = \left( {\sum\limits_{i = 1}^{n}{z_{i}}^{p}} \right)^{1/p}},$can be considered for 0≦p≦1:

$\begin{matrix}{{{{\delta\;\varphi^{k}} - {HY}^{k} + d^{(k)}} = 0},\left. {d^{(k)}}_{p}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.,} & ({Lp})\end{matrix}$If p=0 then (Lp) can involve an exhaustive search, as|z| ₀=card{i:z _(i)≠0}.If 0<p<1, then the problem (Lp) can be non-convex and can also beNP-hard.

If p=1 then (Lp) can turn to (L1) which can be a real-valued l₁ convexlinear programming problem. It can be solved by a linear programmingprocedure, like a simplex method and/or an interior point method.

Restricting d^((k)) to only integer values, a semi-integer linearprogram can be obtained which can be solved by integer programmingmethods.

Alternatively, an orthogonal matching pursuit (OMP) approach can beapplied, which can be less accurate in detection of sparse solutions,but can be faster than l₁ and therefore, better run in real time.Applying QR factorization to the matrix H

$\begin{matrix}{{{QH} = \begin{bmatrix}L^{T} \\0\end{bmatrix}},} & ({LQ})\end{matrix}$where L can be a low triangular 4 by 4 matrix, 0 can stand for a zeromatrix of appropriate size, e.g. (n−4)×4 in this case, Q can be a n×northogonal housholder matrix. Then presenting it in the block form

${Q = \begin{bmatrix}Z \\F\end{bmatrix}},{Z \in R^{4 \times n}},{F \in R^{{({n - 4})} \times 4}},$the following identity can be obtainedFH=0.

The last identity can mean that F can be an annihilating matrix for H.Multiplying both sides of the linear system (MCS) by the matrix F andignoring noise, the following system can be obtained:Fd=b  (Resid)where b=Fδφ^(k), a superscript ^(k) can be ignored for simplicity:d≡d ^(k).

Then, the problem (P) to find the sparsest solution of the linear system(Resid) can be obtained. The sparsest solution of (Resid) can mean thesolution having the least number of entries in its support setS={i:d _(i)≠0}.

The resulting support set of least cardinality can be the set ofchannels affected by cycle slips in the original formulation of theproblem.

The problem (P) can be solved by the orthogonal matching pursuit (OMP)algorithm. It can operate like shown below.

Step 0: Initialize the residual r⁽⁰⁾=b, and initialize the estimate ofthe support set S⁽⁰⁾≠Ø.

Step l=1, 2, . . . : Find the column F_(j) _((k)) of the matrix F thatsolves the problem

${j^{(l)} = {\underset{j}{argmax}\frac{{F_{j}^{T}s^{({l - 1})}}}{F_{j}}}},$and update S^((l))=S^((l−1))∪{j^((l))}, s^((l))=F_(S) _((l)) x^((l))−b,where F_(S) _((l)) can be the sub-matrix of F consisting of columnsF_(j) with indices jεS^((l)).

The steps can be repeated until stopping criterion is satisfieds ^((l)) ^(T) s ^((l))≦σ².  (SC)

That can be a kind of so-called greedy algorithms, the index includedinto the support set may not be taken out of the set.

Now a connection between an application of the OMP algorithm to theproblem (P) and the first isolation procedure (A) can be established.Ignoring the weighting matrix W, becauseH:=

H,b:=

b, where

=W can always be set,Y=(H ^(T) H)⁻¹ H ^(T)δφ,r=δφ−(H ^(T) H)⁻¹ H ^(T)δφ,can be obtained, wherein superscripts ^(k) can be ignored forsimplicity. Taking into account (LQ) factorization,

$\begin{matrix}{r = {{{\delta\varphi} - {{Q^{T}\left\lbrack \frac{L^{T}}{0} \right\rbrack}{\left( {LL}^{T} \right)^{- 1}\left\lbrack L \middle| 0 \right\rbrack}Q\;\delta\;\varphi}} =}} \\{= {{{\delta\;\varphi} - {{Q^{T}\begin{bmatrix}{\; I\;} & {\mspace{11mu} 0} \\0 & {\mspace{11mu} 0}\end{bmatrix}}Q\;{\delta\varphi}}} = {{Q^{T}\begin{bmatrix}{\; 0\;} & {\mspace{11mu} 0} \\0 & {\mspace{11mu} I}\end{bmatrix}}Q\;\delta\;\varphi}}} \\{= {{{{\left\lbrack Z^{T} \middle| F^{T} \right\rbrack\begin{bmatrix}{\; 0\;} & {\mspace{11mu} 0} \\0 & {\mspace{11mu} I}\end{bmatrix}}\left\lbrack \frac{Z}{F} \right\rbrack}\delta\;\varphi} = {F^{T}F\;\delta\;\varphi}}} \\{{= {F^{T}b}},}\end{matrix}$can be obtained, and taking into account the last identity, i.e.r=F^(T)b, it can be seen that the selection of the index j^((l)) at thestep k for l=1 looks pretty much similar to the selection of the maximumresidual entry, i.e. max, in the first isolation procedure. Using morealgebra, it can be proved that using OMP for the problem (P) can bepractically equivalent, up to some minor details, to the first isolationprocedure.

The advantage of this OMP algorithm can be its low computationalcomplexity compared with other methods.

Furthermore, it can be proved, that an application of an exhaustivesearch l₀-optimization, i.e. solving the Lp for p=0 can be equivalent toan application of the second isolation procedure (B).

In addition to an ordinary OMP scheme, the last iteration of OMP can beconcluded with any of suitable integer valued least square detectors,such as ZF, MMSE, MLD, or spherical, to obtain integer values of d^(k).

The solution of the problem (L1) or, which can be equivalent, thesolution of the problemFd=b,|d| ₁→min  (L1′)can allow for more efficient isolation of cycle slips than it can beprovided by the first isolation procedure, equivalently OMP, and lesscomputationally hard isolation than it can be provided by the secondisolation procedure, equivalently l₀ optimization.

FIG. 4 shows a schematic diagram of a system 400 for velocitydetermination of a wireless transmitter 401. The system 400 comprises awireless transmitter 401, first wireless receiver 403, a second wirelessreceiver 405, a third wireless receiver 407, an i^(th) wireless receiver409, an n^(th) wireless receiver 411, a velocity vector v 413, and aserver 415. The wireless transmitter 401 can comprise an antenna.

The wireless transmitter 401 or mobile transmitter and several wirelessreceivers 403, 405, 407, 409, 411 can be located at fixed positions. Thesmall arrows can indicate projections of the velocity vector v 311,shown as a large arrow, onto the line of sight (LOS) lines or vectors.

The wireless transmitter 401 or mobile transmitter can transmit radiosignals to be received by several wireless receivers 403, 405, 407, 409,411 or receivers R_(i), i=1, . . . , n, total number of receivers can ben.

The local clocks of the wireless receivers 403, 405, 407, 409, 411 canbe supposed to be synchronized. Each carrier wave signal received by thewireless receivers 403, 405, 407, 409, 411 can be tracked by its ownPLL. Each PLL can generate the carrier phase measurement φ_(i) ^((k))where k can be the number of sequential time moments, k=1, 2, . . . .The carrier phases can then be sent to the processing server 415.

The system 400 for velocity determination of a wireless transmitter 401in FIG. 4 can be interpreted as an inverse system to the system 300 forvelocity determination of a wireless receiver 100 in FIG. 3. Thevelocity vector v 413 of the wireless transmitter 401 can be determinedanalogously as the velocity vector v 311 of the wireless receiver 100 byexchanging wireless transmitters by wireless receivers and vice versa.

The system 400 therefore supposes an operational mode inverse to thesystem 300.

FIG. 5 shows a schematic diagram 500 of distances versus time between awireless receiver and a wireless transmitter. The diagram 500 comprisesa graph 501 indicating a precise distance between the wireless receiverand the wireless transmitter, a graph 503A indicating a first carrierphase measurement distance between the wireless receiver and thewireless transmitter, a graph 5038 indicating a second carrier phasemeasurement distance between the wireless receiver and the wirelesstransmitter, a first distance deviation 505A between the precisedistance and the first carrier phase measurement distance, a seconddistance deviation 505B between the precise distance and the secondcarrier phase measurement distance, and a distance difference 507between the first carrier phase measurement distance and the secondcarrier phase measurement distance.

The first distance deviation 505A between the precise distance and thefirst carrier phase measurement distance can relate to a carrier phaseambiguity. The second distance deviation 505B between the precisedistance and the second carrier phase measurement distance can relate toa changed carrier phase ambiguity. The distance difference 507 betweenthe first carrier phase measurement distance and the second carrierphase measurement distance can relate to an occurrence of a cycle slipof a phase locked loop.

Carrier phase measurements can be affected by jumps. The graph 501 candenote an ideal carrier phase depending on a position of an objectand/or a variation of a clock shift. The graphs 503A, 503B canillustrate measured carrier phases affected by one cycle slip.

The graphs 501, 503A, 503B can illustrate a time dependency of a carrierphase ambiguity in time. They can indicate that a PLL tracking carrierphase got disturbed and after settling, i.e. an end of a transientprocess, the PLL got settled at different stable point. This phenomenoncan be called a cycle slip (CS). A disturbance of the PLL operation canbe caused by short term shading due to bodies passing by the receiverantenna, mechanical shock affecting a local crystal oscillator, or othernatural reasons.

The presence of a CS, taking arbitrary integer values, can make itdifficult to apply the measurements equation (M) for determination of avelocity vector as the equation (M) can be derived under assumption ofan absence of CSs.

A correct detection and compensation or isolation of CSs can be veryimportant. It is desirable to detect CSs with high probability, like0.999. This leads to a high sensitivity of the CS detector (CSD). Makingthe CSD too sensitive, fault alarms can occur. The CSD can detect CSswith very high probability producing a large number of fault alarms.Fault alarms can be not so undesirable as lost CSs, but also notdesirable, as they can disturb a smooth behavior of the system.Therefore, a reliable CSD can be desirable, while not producing largenumber of fault alarms.

High precision global navigation satellite system (GNSS) receivers canoperate in accordance to this operation scheme. Transmitters can bemounted e.g. at the navigation satellites of the global positioningsystem GPS, the global navigation satellite system GLONASS, and/or theglobal navigation satellite system Galileo.

Precise navigation can be based on simultaneous tracking and processingof code-phase, carrier-phase, and/or Doppler frequency observablesmeasured for a plurality of satellites, allowing for precise positioningand velocity determination.

An challenging issue for precise positioning can be a correct andreliable carrier phases integer ambiguity resolution. Lost cycle slipscan prevent from a desired operation of estimating filters. Therefore,cycle slips detection, isolation and/or correction can be considered asan important challenge of maintaining an operational integrity.

FIG. 6 shows a schematic diagram 600 of distances versus time between awireless receiver and a wireless transmitter. The diagram 600 comprisesa graph 601 indicating a precise distance between the wireless receiverand the wireless transmitter, a graph 603A indicating a first carrierphase measurement distance between the wireless receiver and thewireless transmitter, a graph 603B indicating a second carrier phasemeasurement distance between the wireless receiver and the wirelesstransmitter, a graph 603C indicating a third carrier phase measurementdistance between the wireless receiver and the wireless transmitter, afirst distance deviation 605A between the precise distance and the firstcarrier phase measurement distance, a second distance deviation 605Bbetween the precise distance and the second carrier phase measurementdistance, a third distance deviation 605C between the precise distanceand the third carrier phase measurement distance, a first distancedifference 607A between the first carrier phase measurement distance andthe second carrier phase measurement distance, and a second distancedifference 607B between the second carrier phase measurement distanceand the third carrier phase measurement distance. The diagram 600further comprises a graph 609 indicating a noisy pseudo-rangemeasurement distance.

The first distance deviation 605A between the precise distance and thefirst carrier phase measurement distance can relate to a carrier phaseambiguity. The second distance deviation 605B between the precisedistance and the second carrier phase measurement distance can relate toa changed carrier phase ambiguity. The third distance deviation 605Cbetween the precise distance and the third carrier phase measurementdistance can relate to a further changed carrier phase ambiguity.

The first distance difference 607A between the first carrier phasemeasurement distance and the second carrier phase measurement distancecan relate to an occurrence of a cycle slip of a phase locked loop. Thesecond distance difference 607B between the second carrier phasemeasurement distance and the third carrier phase measurement distancecan relate to a further occurrence of a cycle slip of a phase lockedloop.

FIG. 7 shows a schematic diagram 700 of a carrier phase processing by afilter 701. The diagram 700 comprises the filter 701, an input phase703, and an output phase 705.

The input phase 703 can relate to a measured carrier phase {circumflexover (φ)}_(i) ^((k)). The output phase 705 can relate to a filteredcarrier phase φ_(i) ^((k)).

The carrier phase measurement can pass through the smoothing filter 701.Each filter 701 in a bank can serve for each wireless transmitterseparately.

In an implementation form, each carrier phase measurement of the i^(th)transmitter {circumflex over (φ)}_(i) ^((k)) can be directed from a PLLto the smoothing and/or predicting filter 701, e.g. a Kalman filter, asshown in FIG. 7.

The carrier phase φ_(i) ^((k)) taken from the filter 701 can be smoothedaccording to the dynamic model of the filter 701.

It can e.g. be assumed, that the filter 701 is of third order. Then thestate space of each filter 701 can be three dimensional, comprisingthree dimensional vectors

$\Phi_{i}^{(k)} = {\begin{pmatrix}\varphi_{i}^{(k)} \\{\overset{.}{\varphi}}_{i}^{(k)} \\{\overset{¨}{\varphi}}_{i}^{(k)}\end{pmatrix}.}$

The filter 701 can sequentially calculate an extrapolated and/orpredicted state Φ _(i) ^((k+1))=FΦ _(i) ^((k)) and a corrected stateΦ_(i) ^((k+1))=Φ _(i) ^((k+1)) +K({circumflex over (φ)}_(i) ^((k+1))−φ_(i) ^((k+1))).

The transition matrix F can be constructed according to the dynamicmodel laid in the basis of the filter 701. One of frequently used modelscan have the matrix

${F = \begin{bmatrix}1 & \tau & {1\text{/}2\tau^{2}} \\0 & 1 & \tau \\0 & 0 & 1\end{bmatrix}},$where τ can be the time step. The gain coefficient vector K can beconstructed either as a limit of a sequence of iteratively re-calculatedKalman filter gains, or adjusted adaptively during tuning. The residualε_(i) ^((k+1))=({circumflex over (φ)}_(i) ^((k+1))−φ _(i) ^((k+1))) canmean a disagreement between a predicted carrier phase φ _(i) ^((k+1))and raw carrier phase taken from the PLL {circumflex over (φ)}_(i)^((k+1)). The residual can be compared against a threshold |ε_(i)^((k+1))|<T (CT) Satisfied inequality (CT) can be considered as normalsteady state operation, which can mean that the object is either static,or it is steadily moving allowing the PLLs continuously track avariation of carrier phases. A violated inequality can be considered asan indication or sign of a cycle slip.

In another implementation form, each PLL can be considered as a filterperforming prediction and/or correction operations. The value of theerror signal can be analyzed before the feedback is locked. The PLL canraise an alarm flag if the error signal exceeds some thresholdindicating possibility of a cycle slip.

A disadvantage of this approach, considering each measurement channelindependently, can be that its performance can be highly dependent onthe agreement between the expected normal motion of the object anddynamic model of the filter 701. In other words, that can be pretty hardto identify whether the fast variation of the carrier phase, e.g.indicated as a disagreement between expected and received carrier phase,is caused by a fast and/or aggressive motion of the object, or by acycle slip.

A fast variation of the carrier phase caused by the movement of theobject can lead to a fast variation of all carrier phase measurements,so an alternative approach can be based on simultaneous multichannelanalysis of the carrier phase incremental, checking whether they allchange in agreement and their variation is consistent with a changing ofthe object's position. In order to perform this check, the number ofmeasurements can be greater than 4. In other words, the linear system(M) can be over-determined.

So, alternatively to the independent channel analysis described above,the set of measurements (M) can be considered. A least square solutioncan be calculated Y^(k)=(H^(T)WH)⁻¹H^(T)Wδφ^(k), with W=C⁻¹, C can bethe errors covariance matrix. Then residuals can be calculatedr^(k)=δφ^(k)−(H^(T)WH)⁻¹H^(T)Wδφ^(k), and squared with the weightingmatrix W, forming the value χ_(est) ²=r^(k) ^(T) Wr^(k).

An absence of cycle slips can mean that only noise is presented in theerrors vector. In this case, an estimated χ_(est) ² value can satisfythe χ² statistics distribution with a number of degrees freedom equal tondf=n−4. A comparison with the χ² statistical threshold χ_(est) ²<T_(χ)₂ (α,ndf), (NoCS) corresponding to a certain confidential probability αand a number of degrees ndf, as there are n observables and 4 parametersto be estimated, can be performed to check whether an assumption aboutan absence of cycle slips is justified. Typical value of α can be0.95-0.999.

Otherwise, if the (NoCS) inequality does not hold, the hypothesis of noslips can have a probability of less than 1−α and the statement thatcycle slips are presented can be assumed to be proved.

After a presence of CSs is proved, i.e. the detection gave positiveanswer, an alarm flag can be raised and an isolation procedure canstart. The isolation procedure can be aimed to find which PLL, or PLLs,produces carrier phase measurement affected by cycle slips at timeinstant k+1. In other words, the isolation procedure can try to answerthe question for which i the condition d_(i) ^(k)≠0, or equivalently forwhich PLL N_(i) ^(k+1)≠N_(i) ^(k) holds.

There can be at least two ways to perform an isolation procedure havingresults of a least squares minimization.

A first isolation procedure (A) can be based on an assumption thatchannel corresponding the maximum value of the residual entry is

$i^{*} = {\underset{i}{\arg\;\max}{{r_{i}^{(k)}}.\mspace{25mu}({Max})}}$

The channel i* can then be excluded from the system (M). A new system(M) can be considered having dimensions n′×4, where n′=n−1 and LMScalculations repeat ending again with checking the inequality (NoCS)with new ndf′=ndf−1. If the inequality (NoCS) is satisfied, then asingle CS can be found and isolated correctly. Otherwise, either theassumption that CS produces maximum residual entry can be invalid, orthere may be no unique CS. The procedure can repeat until either thecondition (NoCS) is satisfied, or a new ndf′=0 and no redundancy is leftfor analysis.

In the first case, all cycle slips, probably excluding excessive numberof channels which have not been actually affected, can have been foundwith high probability. In the second case, the procedure can have endedwithout results. Channels affected by cycle slips may not have beenidentified and an operation of the whole system can be subject to resetwith an alarm flag.

A second isolation procedure (B) can run an exhaustive search amongchannel indices, excluding them one by one, then, if necessary,combinations of various pairs of indices, then, if necessary, triplesand so on. The procedure can stop if for remaining channels with reducednumber n′<n, the (NoCS) condition holds (with n substituted by n′). Tore-calculate the least square solutions, a previous solution can bemodified applying low rank modifications.

The isolation procedure can stop also if there is no more redundancy tocheck residuals, which can be zero if n′=4. In this case the system canbe subject to reset and the alarm flag can be raised. Velocity may notbe determined reliably in this case.

An advantage of isolation procedure A can be the simplicity and lowcomputational cost. A disadvantage of the isolation procedure A can bethe low accuracy when detecting an affected channel. An advantage of theisolation procedure B can be the good accuracy of isolation of theaffected channel or channels comparing with procedure A. A disadvantageof the isolation procedure B can be the high computational cost whichcan be caused by an exhaustive search involved in the calculations.

A CS isolation procedure combining high accuracy, i.e. probability ofcorrect CS detection, and relatively low computational cost isdesirable.

An isolation procedure based on a compressive sensing approach can aimto improve the accuracy and reduce the computational cost of isolationprocedures.

If redundancy is high enough, like 16-20, and number of cycle slips islow, like 1-2, then not only isolation, but also correction of CSs canbe expected.

High precision Global Navigation Satellite Systems (GNSS) receivers canuse range measurements generated in the two scales of code phase andcarrier phase.

Code phase, or pseudo-range, measurements can be connected with thegeometric distance from a GNSS antenna to the satellites by thefollowing relationship:

${\rho_{sr}(t)} = {\sqrt{\left( {{x_{s}(t)} - {x_{r}(t)}} \right)^{2} + \left( {{y_{s}(t)} - {y_{r}(t)}} \right)^{2} + \left( {{z_{s}(t)} - {z_{r}(t)}} \right)^{2}} + {c\left( {{\Delta_{s}(t)} - {\Delta_{r}(t)}} \right)} + {ɛ_{sr}(t)}}$ρ_(sr) can be the pseudo-range measured by the receiver r for thesatellite s which can be a GPS or a GLONASS satellite or can belong toanother satellite system. In other words, it can be a pseudo-rangebetween the satellite and the receiver. The prefix pseudo can mean thatthe range can be affected by clock errors.

Δ_(s) can be a clock difference between the local oscillator of thesatellite and the system time standard. Δ_(r) can be a clock differencebetween the local oscillator of the receiver and the system timestandard. x_(s), y_(s), z_(s) can be the satellite's position in theearth centered earth fixed (ECEF) Cartesian frame. x_(r), y_(r), z_(r)can be the receiver's position in ECEF, which can be determined as aresult of a navigation task. ε_(sr) can be a measurement error.c=299792458 m/sec can be the light speed in the vacuum. (t) can be thesymbol denoting dependency on time. Time can be supposed to be discrete.

The error ε_(sr)(t) can include a white noise component, an atmosphericcomponent, a multipath component and other errors. The noise componentcan belong to the range 1-10 meters. This can explain why simplenon-professional navigators using only pseudo-ranges can be accurate upto several meters.

Another measurements scale can be the carrier phase. A measurementequation connecting the carrier phase with the receiver's position canbe:

${\phi_{sr}(t)} = {{\frac{1}{\lambda_{s}}\sqrt{\left( {{x_{s}(t)} - {x_{r}(t)}} \right)^{2} + \left( {{y_{s}(t)} - {y_{r}(t)}} \right)^{2} + \left( {{z_{s}(t)} - {z_{r}(t)}} \right)^{2}}} + {f_{s}\left( {{\Delta_{s}(t)} - {\Delta_{r}(t)}} \right)} + N_{s} + {\xi_{sr}(t)}}$φ_(sr) can be the carrier phase measurement. λ_(s) and f_(s) can bewavelength and carrier frequency respectively,

$\lambda_{s} = {\frac{c}{f_{s}}.}$

Assuming that the receiver can operate on the first frequency band L1,f_(s)=1575.42 MHz for all GPS satellites and f_(s)=1602+k×0.5625 MHz forGLONASS satellites can be obtained, where k can be the so called letternumber connected to the GLONASS satellite index number. Differentsatellites can have different letters because GLONASS can exploit FDMAto distinguish between satellites.

N_(s) can be the carrier phase ambiguity which can be an unknown integervalue. ξ_(sr) can be the carrier phase measurement error.

The error ξ_(sr)(t) can include a white noise component, an atmosphericcomponent, a multipath component and other errors. As opposite to thepseudo-range noise, the carrier phase noise component can belong to therange 0.001-0.01 meters. Using carrier phase measurements can give thekey for high precision navigation provided by professional geodeticgrade GNSS receivers.

The main obstacle to straightforward using of carrier phase measurementsto get centimeter accuracy of positioning can be the presence of carrierphase ambiguity N_(s). Its nature can be in a difference between initialphases of a heterodyne of the receiver and a generator of the satellite.Moreover, the PLL's tracking carrier phase can be accurate up to anunknown number of cycles. This can explain why ambiguity can take aninteger value.

The dependency on time of the distance to the satellite and code- andcarrier phase measurements after compensation for time scale differencescan be illustrated by FIG. 6.

The horizontal axis can indicate time. The vertical axis can indicatedistance. The precise distance to the satellite can be shown by graph601. The graph 609 can show pseudo-range measurements affected by noise.Carrier phase measurements can be shown by graphs 603A, 603B, 603C. Theshift between graphs 603A, 603B, 603C and graph 609 can be due to thecarrier phase ambiguity.

There are two jumps in carrier phase measurements plot in graphs 603A,603B, 603C. These can illustrate a time dependency of the carrier phaseambiguity in time. They can indicate that the PLL tracking carrier phasegot disturbed and after settling, i.e. an end of a transient process,the PLL got settled at a different stable point. This phenomenon can becalled a cycle slip (CS). The presence of a CS, taking arbitrary integervalues, can make it difficult to filter and estimate the carrier phaseambiguity. Lost CSs can violate a smooth behavior of a precisenavigation engine.

A correct detection, compensation, and/or isolation of CSs can be achallenge. It can be desirable to detect CSs with high probability, e.g.0.999. This can dictate a high sensitivity of a CS detector (CSD).Making CSD too sensitive, a possibility of fault alarms is allowed. CSDcan detect CSs with very high probability producing quite a large numberof fault alarms. Fault alarms may not be so undesirable as lost CSs, butcan also be not desirable, as they can disturb a smooth behavior of anambiguity estimator. In short words, a reliable CSD can be desirable,yet not producing a large number of fault alarms.

Let n be the number of satellites tracked by the receiver. LetX(t)=(x_(r)(t), y_(r)(t), z_(r)(t))^(T) be the solution obtained by thenavigator at time instance t.

Let H be the matrix of linearized, in the neighborhood of the pointX(t), system of carrier phase measurements, called also a directionalcosine matrix. It can vary very slowly in time and it can be consideredas almost constant. So, the dependency on time can be omitted,

$H = \begin{bmatrix}h_{1x} & h_{1y} & h_{1z} & 1 \\h_{2x} & h_{2y} & h_{2z} & 1 \\\ldots & \ldots & \ldots & \ldots \\h_{nx} & h_{ny} & h_{nz} & 1\end{bmatrix}$with (h_(sx), h_(sy), h_(sz))^(T) being the directional cosines vector,or the vector of the line of sight (LOS) from the receiver to thesatellite. The fourth column of the matrix can be composed of units asthe variables to be determined can be x_(r), y_(r), z_(r), cΔ_(r), i.e.three Cartesian components of the position and time shift of thereceiver local oscillator expressed in meters.

Let Λ=diag(λ₁, λ₂, . . . , λ_(n)) be the diagonal matrix of carrierwavelengths. Let D be the time difference operator Dφ(t)=φ(t+1)−φ(t).

The system of linearized equations of carrier phase measurements withrespect to the position X(t+1) can take the formΛDφ(t)−R(t)≡Y(t)=HDX(t)+DN(t)+Dξ(t) (LinEq)

${R_{s}(t)} = \sqrt{\left( {{x_{s}(t)} - {x_{r}(t)}} \right)^{2} + \left( {{y_{s}(t)} - {y_{r}(t)}} \right)^{2} + \left( {{z_{s}(t)} - {z_{r}(t)}} \right)^{2}}$If cycle slips are absent, then DN(t)≡0 (No CS)

A possible approach to CSD can be like follows. Assuming no CSs DN(t)≡0try to solve the over-determined system with weights W Y(t)=HDX(t)(LinEq-NoCS) having the result DX(t)=(H^(T)WH)⁻¹H^(T)WY(t) Then checkresiduals r≡Y(t)−HDX(t)=(I−H(H^(T)WH)⁻¹H^(T)W)Y(t), calculate weightedsum of squares χ²=r^(T)Wr=Y(t)^(T)(W−WH(H^(T)WH)⁻¹ H^(T)W)Y(t), andcompare with the χ² statistics threshold T_(χ) ₂ (α,ndf) correspondingto a certain confidence probability α and a number of degrees of freedom(ndf) which is n−4, as there are n equations and 4 variables. Typicalvalue of α=0.954÷0.999.

An assumption about no cycle slips can be approved if the followingcondition holds: χ²<T_(χ) ₂ (ε,n−4) (NoCS-approved) Otherwise, if thisinequality does not hold, the hypothesis of no slips can have aprobability of less than 1−α. After presence of CSs is proved, i.e.detection gave a positive answer, the alarm flag can be raised andisolation procedure can start.

The isolation procedure can be aimed to find which satellite, orsatellites, has a carrier phase measurement affected by a cycle slips atthe time instant t+1. In other words, the isolation procedure can try toanswer the question which DN_(s)(t)≠0, or equivalently for whichsatellite N_(s)(t)≠N_(s)(t+1)

Usually, an isolation procedure can run an exhaustive search amongsatellites indices, excluding them one by one, then, if necessary,combinations of various pairs of indices, then, if necessary, triplesand so on. The procedure can stop if for remaining satellites, reducednumber n′<n, the (NoCS-approved) condition holds with n substituted byn′. To re-calculate (LinEq-NoCS) equations it is desirable to modify aprevious solution applying a low rank modifications.

The isolation procedure can stop also if there is no more redundancy tocheck residuals, which will be zero if n′=4. In this case the system canbe subject to reset and all residuals estimators can start to filterfrom the scratch.

If the redundancy is high enough, like 16-20, and the number of cycleslips is low, like 1-2, then not only isolation can be expected, butalso correction of CSs.

In the following, a first difference of measurements of two receivers, arover and a base can first be calculated. It can be possible that in thefirst difference common errors like ephemeris errors and satellitesclock errors Δ_(s)(t) can vanish.

In the following, the system (LinEq) can be considered. ConsideringDN(t) as an error affecting only a few of the linear equations, a linearprogramming decoding procedure can be applied. In this case it can looklike

$\begin{matrix}{{{{Y(t)} - {{HDX}(t)} + {{DN}(t)}} = 0},\left. {{{DN}(t)}}_{1}\rightarrow\min\limits_{{{{DX}{(t)}} \in R^{4}},{{{DN}{(t)}} \in R^{n}}} \right.} & ({L1})\end{matrix}$or, restricting DN(t) to only integer values DN(t)εZ^(n) where Z^(n) canbe an integer lattice

$\begin{matrix}{{{{Y(t)} - {{HDX}(t)} + {{DN}(t)}} = 0},\left. {{{DN}(t)}}_{1}\rightarrow\min\limits_{{{{DX}{(t)}} \in R^{4}},{{{DN}{(t)}} \in Z^{n}}} \right.} & \left( {{L1}\mspace{14mu}{SI}} \right)\end{matrix}$

The real-valued L1 optimization problem (L1) can be solved by linearprogramming procedures, like a simplex method, and/or an interior pointmethod.

Restricting DN(t) to only integer values, a semi-integer linear program(L1-SI) can be obtained.

Alternatively, an orthogonal matching pursuit (OMP) approach can beapplied, which can be less accurate in detection of sparse solutions,but can be much faster than LP and so can better run in real time. Forthe sake of brevity, it can be defined x=DX(t), d=−DN(t), b=−Y(t) and(L1) can be rewritten as

$\begin{matrix}{{{{Hx} + d} = b},\left. {d}_{1}\rightarrow\min\limits_{{x \in R^{4}},{d \in R^{n}}} \right.} & \left( {L1}^{\prime} \right)\end{matrix}$

Applying a QR factorization to the matrix H,

${QH} = \begin{bmatrix}L^{T} \\O\end{bmatrix}$can be obtained where L can be a low triangle 4×4 matrix, O can be a(n−4)×4 zero matrix, Q can be an n×n orthogonal matrix, e.g. ahouseholder matrix. Then, presenting the last matrix in a block form

${Q = \begin{bmatrix}Z \\F\end{bmatrix}},{Z \in R^{4 \times n}},$FεR^((n−4)×n) the following identity can be obtained FH=0 (Annihilator)

The last identity can mean that F can be an annihilating matrix for H.Multiplying both sides of the linear system (L1′) by the matrix F andapplying a scheme, the problem to find the sparsest solution of thelinear system can be obtained:

Fd=y (Residual) where y=Fb. The sparse solution of the (Residual) can beobtained by applying an OMP algorithm. In addition to an ordinary OMPscheme, the last iteration of OMP can be concluded with integer valuedleast square detectors, such as ZF, MMSE, MLD, or spherical, in order tohave integer values of d, and so DN(t).

In an implementation form, the patent application relates to acompressive sensing based method for cycle slips detection andcorrection in PLLs used in velocity determination systems.

In an implementation form, the patent application relates to thebehavior of the PLL used in velocity determination systems, especiallythe anomalous phase variation detection.

In an implementation form, the patent application relates to acompressive sensing based method for cycle slips detection andcorrection in GNSS receivers.

In an implementation form, the patent application is based on using theconcepts of sparsity of a cycle slips vector and linear programmingdecoding, as cycle slips can occur seldom and can affect only a fewcarrier phase measurements among a plurality of measurements.

In an implementation form, the patent application can be applied to dataintegrity maintaining in motion detection systems. It can also beapplied to data integrity maintaining in satellite navigation receivers.

In an implementation form, the patent application relates to a methodfor cycle slips detection and correction based search for a most sparseerror vector.

In an implementation form, a linear programming approach is used.

In an implementation form, a semi-integer linear programming is used.

In an implementation form, an OMP enhanced by integer search at its laststep is used.

In an implementation form, the patent application is based on exploitinga linear programming approach to solve a cycle clips detection problem.

In an implementation form, the patent application is based on exploitinga semi-integer linear programming approach for detection and/orcorrection of cycle slips.

In an implementation form, the patent application is based on exploitingan OMP algorithm for cycle slips detection and/or correction.

In an implementation form, the patent application is based on exploitingan OMP algorithm enhanced by an integer search at its last iteration forcycle slips detection and/or correction.

What is claimed is:
 1. A wireless receiver capable of determining itsvelocity with respect to a plurality of wireless transmitters, thewireless receiver comprising: a communication interface configured toreceive a plurality of carrier signals originating from the plurality ofwireless transmitters; and a processor configured to: determine aplurality of carrier phases of the carrier signals at two different timeinstants, determine a plurality of carrier phase differences from thedetermined plurality of carrier phases for each carrier signal betweenthe two different time instants, determine a location matrix indicatinga geometric relationship between a location of the wireless receiver andlocations of the plurality of wireless transmitters, and determine thevelocity of the wireless receiver based on an optimization procedurethat includes the following equation: δφ^(k) − HY^(k) + d^((k)) = 0where δφ^(k) denotes a vector comprising the plurality of carrier phasedifferences, H denotes the location matrix, Y^(k) denotes a vectorcomprising the velocity of the wireless receiver, d^((k)) denotes avector comprising a number of cycle slip values, and k denotes a timeinstant index.
 2. The wireless receiver according to claim 1, whereinthe optimization procedure further includes the following equation:$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein | |₁ denotes the l₁-norm of a vector, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. 3.The wireless receiver according to claim 1, wherein the optimizationprocedure further includes the following equation:$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in Z^{n}}} \right.$wherein | |₁ denotes the l₁-norm of a vector, R⁴ denotes the4-dimensional set of real numbers, Z^(n) denotes the n-dimensionalinteger lattice and n denotes the number of wireless transmitters. 4.The wireless receiver according to claim 1, wherein the optimizationprocedure further includes the following equation:$\left. {d^{(k)}}_{p}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein | |_(p) denotes the l_(p)-norm of a vector, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. 5.The wireless receiver according to claim 1, wherein the processor isconfigured to perform the optimization procedure using a linearprogramming method, a semi-integer linear programming method or anorthogonal matching pursuit method.
 6. The wireless receiver accordingto claim 1, wherein the processor is configured to determine theplurality of carrier phases of the carrier signals by comparing theplurality of carrier signals with a plurality of reference signals. 7.The wireless receiver according to claim 1, wherein the communicationinterface comprises a plurality of phase-locked-loops configured toreceive the plurality of carrier signals originating from the pluralityof wireless transmitters.
 8. The wireless receiver according to claim 1,wherein the communication interface is configured to receive theplurality of carrier signals according to afrequency-division-multiple-access scheme, time-division-multiple-accessscheme or a code-division-multiple-access scheme.
 9. The wirelessreceiver according to claim 1, wherein the communication interface isconfigured to selectively receive a plurality of carrier signals havingdifferent carrier frequencies, carrier phase differences, or carrierphase Doppler frequencies.
 10. A method for determining a velocity of awireless receiver with respect to a plurality of wireless transmitters,the method comprising: receiving a plurality of carrier signalsoriginating from the plurality of wireless transmitters by the wirelessreceiver; determining a plurality of carrier phases of the carriersignals at two different time instants by the wireless receiver;determining a plurality of carrier phase differences from the determinedplurality of carrier phases for each carrier signal between the twodifferent time instants by the wireless receiver; determining a locationmatrix indicating a geometric relationship between a location of thewireless receiver and locations of the plurality of wirelesstransmitters; and determining the velocity of the wireless receiverbased on an optimization procedure that includes the following equation:δφ^(k) − HY^(k) + d^((k)) = 0 where δφ^(k) denotes a vector comprisingthe plurality of carrier phase differences, H denotes the locationmatrix, Y^(k) denotes a vector comprising the velocity of the wirelessreceiver, d^((k)) denotes a vector comprising a number of cycle slipvalues, and k denotes a time instant index.
 11. The method according toclaim 10, wherein the optimization procedure further includes thefollowing equation:$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein | |₁ denotes the l₁-norm of a vector, R⁴ denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. 12.The method according to claim 10, wherein the optimization procedurefurther includes the following equation:$\left. {d^{(k)}}_{1}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in Z^{n}}} \right.$wherein | |₁ denotes the l₁-norm of a vector, R⁴ denotes the4-dimensional set of real numbers, Z^(n) denotes the n-dimensionalinteger lattice and n denotes the number of wireless transmitters. 13.The method according to claim 10, wherein the optimization procedurefurther includes the following equation:$\left. {d^{(k)}}_{p}\rightarrow\min\limits_{{Y^{k} \in R^{4}},{d^{k} \in R^{n}}} \right.$wherein | |_(p) denotes the l_(p)-norm of a vector, denotes the4-dimensional set of real numbers, R^(n) denotes the n-dimensional setof real numbers and n denotes the number of wireless transmitters. 14.The method according to claim 11, wherein the optimization procedure isperformed using a linear programming method, a semi-integer linearprogramming method or an orthogonal matching pursuit method.
 15. Anon-transitory computer readable medium containing instructions forperforming the method according to claim 10 when executed by at leastone processing device.
 16. The method according to claim 10, wherein theoptimization procedure is performed using a linear programming method, asemi-integer linear programming method or an orthogonal matching pursuitmethod.
 17. The method according to claim 10, wherein the plurality ofcarrier phases of the carrier signals are determined by comparing theplurality of carrier signals with a plurality of reference signals. 18.The wireless receiver according to claim 2, wherein the communicationinterface comprises a plurality of phase-locked-loops configured toreceive the plurality of carrier signals originating from the pluralityof wireless transmitters.